Geometric Re-Analysis of Classical MDP Solving Algorithms
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909527468670976 |
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| author | Mustafin, Arsenii Pakharev, Aleksei Olshevsky, Alex Paschalidis, Ioannis Ch. |
| author_facet | Mustafin, Arsenii Pakharev, Aleksei Olshevsky, Alex Paschalidis, Ioannis Ch. |
| contents | We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical apparatus, including a transformation that modifies the discount factor $γ$, to improve convergence guarantees for these algorithms in several settings. In particular, one of our results identifies a rotation component in the VI method, and as a consequence shows that when a Markov Reward Process (MRP) induced by the optimal policy is irreducible and aperiodic, the asymptotic convergence rate of value iteration is strictly smaller than $γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Re-Analysis of Classical MDP Solving Algorithms Mustafin, Arsenii Pakharev, Aleksei Olshevsky, Alex Paschalidis, Ioannis Ch. Machine Learning We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical apparatus, including a transformation that modifies the discount factor $γ$, to improve convergence guarantees for these algorithms in several settings. In particular, one of our results identifies a rotation component in the VI method, and as a consequence shows that when a Markov Reward Process (MRP) induced by the optimal policy is irreducible and aperiodic, the asymptotic convergence rate of value iteration is strictly smaller than $γ$. |
| title | Geometric Re-Analysis of Classical MDP Solving Algorithms |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.04203 |